Speaking at a press conference today, Detective Chief Superintendent Stewart Gull said detectives had not yet determined how the latter two sex workers died, but he said neither woman appeared to have been sexually assaulted or strangled.

In a message to the killer, Mr Gull said: "Make contact with Suffolk Police. Clearly you have a significant problem. Give me a call and we can deal with this.

"My appeal is simple. Give yourself up."

As details of the third murder emerged, concern mounted that the killings might not stop there. Police are today continuing a desperate search for 24-year-old Paula Clennell and Annette Nicholls, 29, two prostitutes who remain missing. Despite an avalanche of media coverage since yesterday, neither have come forward.

Mr Gull today said he had "grave concerns" for their welfare and appealed again for any information on their whereabouts.

The pair, who worked the same red light area as the three murdered women, are reported to have vanished from the Suffolk town.

The naked bodies of three young women have been found in the past nine days and the 30 or 40 prostitutes in Ipswich were warned by police to stay off the streets until the killer is caught. Detectives' immediate fears were for the safety of Miss Clennell, who disappeared on Saturday night, and Miss Nicholls, who was last seen by a family member more than a week ago.

Miss Clennell's boyfriend reported her missing late on Sunday. Yesterday police visited several addresses where they thought she might be, but to no avail. However, there was a reported sighting of her on Sunday evening and she is thought to have contacted a friend by mobile phone.

Fearful after the recent killings, the family of Miss Nicholls tried to trace her over the weekend and reported her missing to police yesterday. Police have traced several other prostitutes whom family or friends had been unable to contact.

"We are obviously concerned about the safety of these women," said a police source. "We need to hear from them if they are safe and well. At the moment, they are missing persons, no more than that."

Jacqui Cheer, the assistant chief constable of Suffolk, appealed to the town's prostitutes to stop work in the wake of the murders. "Your welfare is my priority," she said. "My message to you is simple – stay off the streets. If you are out alone at night, you are putting yourself in danger."

She also warned other women on Christmas outings to take special care. "There will be groups of women going out and I would say you have really got to look after each other, plan how you are going to get there and come home together."

The bodies recovered have been those of Tania Nicol, 19, who disappeared on Oct 30. Her naked body was found in a stream at Copdock on Friday. Gemma Adams, 25, who vanished in the early hours of Nov 15, was found in the same stream at Hintlesham on Dec 2.

On Sunday afternoon, the body of Anneli Alderton, 24, was found in a wood at Nacton. None of the women's clothing has been found, apart from a pair of trainers believed to belong to Miss Adams. They are undergoing forensic examination after being found on a tyre company's forecourt near the Portman Road football ground.

Mr Gull said that, apart from a reported sighting at about 10.30pm on Sunday, Miss Clennell was believed to have called a friend's mobile, asking if she knew where she might stay.

"There could be an innocent explanation as to why these two girls are missing," said Mr Gull. "We know, for example, that Paula is of no fixed address and moves between addresses regularly.

"However, in the current climate, we are concerned for their welfare and are making urgent inquiries to locate them."

As night fell and a very visible police presence took to the streets, an Ipswich businessman who had offered £25,000 for information leading to the conviction of the killer doubled his reward.

Graeme Kalbraier, the managing director of the Call Connection call centre, said: "I have a teenage daughter aged 17. I also have an Ipswich workforce of 300, many of whom are girls in their teens and early 20s. I want this killer off the streets."

Police are interviewing many of the almost 400 men in Suffolk on the sex offenders' register. They are also looking at whether the A14 was used by the killer to transport the bodies because all were found in an arc to the south of the town, not far from the trunk road.

Further tests are being carried out to discover exactly how the women were killed. Neither Miss Adams nor Miss Nicol was sexually abused and there were no obvious signs of violence on the bodies.

Officers do not believe the recent killings are connected to the disappearance or murders of five other prostitutes from Ipswich and Norwich over the past 15 years.

But John Bettles, the father of 22-year-old Michelle Bettles whose body was found in woodland four years ago after disappearing from the red light district of Norwich, said he believed his daughter could have been the victim of the serial killer.

"I must admit that the more information that's coming out, and looking at what happened to Michelle and what's happening now, there do seem to be a lot of similarities," said Mr Bettles, 51.

"No-one's ever been caught for Michelle."

Despite the police plea for women to stay off the streets, Simon Aalders, of the Suffolk Drug Action Team which works with prostitutes in Ipswich, said that he doubted they all would.

Despite the dangers, addicts were desperate for the money they needed to feed their habit. "Some women are stopping their activity but some aren't," he said.